Lavinia Corina Ciungu

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The notion of a state is an analogue of a probability measure and was first introduced by Kôpka and Chovanec for MV-algebras and by Riec̆an for BLalgebras. The states have also been studied for different types of non-commutative fuzzy structures such as pseudo-MV algebras, pseudo-BL algebras, bounded R`monoids, residuated lattices and pseudo-BCK(More)
Pseudo-MTL algebras or weak pseudo-BL algebras are non-commutative fuzzy structures which arise from pseudo-t-norms, namely, pseudo-BL algebras without the pseudo-divisibility condition. The aim of this paper is to investigate the properties of pseudo-BL algebras that also hold for pseudoMTL algebras. We will also study some classes of pseudo-MTL algebras(More)
If A is a bounded R -monoid or a pseudo-BL algebra, then it was proved that a subinterval [a, b] of A can be endowed with a structure of an algebra of the same kind as A. Similar results were obtained if A is a residuated lattice and a, b belong to the Boolean center of A. Given a bounded pseudo-hoop A, in this paper we will give conditions for a, b ∈ A for(More)
Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events. In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski’s inclusion-exclusion principle for probabilities on IF-events. Finally, we(More)